Games@Dal 2016: Tanya talks about Cookie Monster Games

Tanya Khovanova shared some work with a bunch of high schoolers (whoa!) on patterns in Cookie Monster games. Cookie Monster games are Nim games where k sticks (cookies) can be removed from multiple heaps. Each ruleset has a different restriction on which sets of piles can be removed from.

She and her students considered rulesets where you can take from...:

No restriction

One-or-all piles

One-or-two piles

Any consecutive piles (assuming the piles are in a list)

One or two consecutive piles

Any set of piles including the first jar

Any odd number of piles. (It turns out that the P positions are the same as in Nim!)

Any set of piles except all of them.

... and more!

In one of these games, she noticed a surprising correlation with an automaton problem! A sequence of the number of P positions is related to the number of new cells born from the Ulam-Warburton automaton. She then looked more closely at other relationships to automaton!

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Combinatorial Game Man

artist: Molly Dannaher

What is This?

This blog is devoted to Combinatorial Game Theory! Combinatorial games are two-player games with no randomness, perfect information (no one has any hidden information) and no draws allowed, though sometimes topics stray into other types of games as well.

Please let me know if you are interested in either writing a guest post or suggesting a topic. I would like this to be more reflective of CGT as a whole and not restrict it to my take on things. Additionally, please help me fill out the table of game properties, either by suggesting games or letting me know about results!